A simple procedure for testing linear hypotheses about the parameters of a nonlinear model using weighted least squares

Abstract

Suppose the same nonlinear function involving k parameters is fit to each of t populations. Suppose further it is of interest to compare a specific parameter of the models across the populations. Such comparisons can be expressed as linear hypotheses about the parameters of the nonlinear models. A weighted linear least squares (WLLS) procedure is proposed to test these linear hypotheses. The advantages and disadvantages of the WLLS procedure are discussed. This procedure is also compared to a nonlinear least squares procedure for testing these hypotheses in nonlinear models.

Keywords:

• Jacobian
• cross-classified design
• covariance analysis
• reparameterization
• growth model